强光与自由电子的相互作用——半导体中载流子的多光子过程

本文讨论了半导体中载流子与laser光的相互作用。把电子运动分成带内运动与带间跃迁两部分后,我们证明了在强光下,电子在带内运动的状态仍可用准动量p来标志,但不再是通常的稳定态,波函数中包含一个描述强迫运动的因子。进一步以带间跃迁或其他带内过程作为微扰,由于在跃迁过程中强迫运动部分也改变,因此伴随着有多光子的吸收或发射。根据一般的讨论,我们计算了由电声子作用引起的自由载流子吸收及由价带到导带的直接多光子跃迁的吸收系数。粗略估计表明,在一些材料中,上述过程引起的双光子吸收是可以被观察到的,特别是Ge中的直接双光子吸收。我们还指出,利用一束laser光射到晶体上后,可以在红外区域看到激子吸收线,从而提高了分辨率,并具体地分析了CdSe中激子吸收的情况。     

二价铁对铁磁共振线宽的影响

本文讨论二价铁对铁氧体的铁磁共振线宽的影响。由于在尖晶石型铁氧体中,二价铁的基态是轨道单态,晶场的直接效应很小。二价铁对铁磁共振性质有显著影响的原因是各向异性交换作用引起二价铁磁矩不与总磁矩平行,因而使得文献[1]中所述的纵分支对共振性质起作用。我们推广文献[1]中的方法,使之适用于强交换耦合体系,并用之计算了二价铁对共振线宽的影响。计算表明,体系间的交换耦合的强弱对线宽的影响很小。对含二价铁反型尖晶石型铁氧体算得的结果解释了[100]方向线宽随温度的变化不出现极大,而在其他方向则出现极大的现象。导出的线宽的各向异性也与实验相符。     

Numerical study of the representation of a totally positive quadratic integer as the sum of quadratic integral squares

Resume Altogether a total of almost 200,000 totally positive numbers from different fields were decomposed into squares; in no case were more than five squares required, although in many cases no number of squares sufficed. For some quadratic fields, from our evidence it would seem safe to completely characterize the couples for whichQ=5 or 0, particularly whenm13; and furthermore, form=17 or 33 it seems possible to characterize all cases whereQ=4, 5, or 0.The whole calculation seems to be pointed toward the result that three squares are sufficient except for special cases. Incidentally, the analytic methods ofSiegel andMaass run parallel to the calculation in that these methods involve the third, fourth, and fifth power of a theta-function. The numberical evidence would therefore suggest that their methods point to an analytic (or even a purely algebraic) proof of the futility of using more than five squares in any case.The work was supported in part by the U. S. National Science Foundation Grant G-4222 and the computer services were contributed by the Argonne National Laboratory of the U. S. Atomic Energy Commission during the summer of 1958. The coding was performed by Mr.Alan V. Lemmon with remarkable economy of length of program and running time.The deepest debt of gratitude is owed to the lateDonald A. (Moll) Flanders whose contributions to the logical design ofGeorge had made the rapid execution of the program possible and whose personal interest made possible the availability of the computer for this work. Donald A. Flanders in Memoriam (1900–1958).     

核子结构对质子俘获μ- 介子的影响

本文指出由于费曼—盖尔曼理论中弱相互作用与电磁相互作用的相似性,矢量耦合部分对质子俘获μ^-介子的贡献与核子的电磁形状因子相联系。本文给出了在重正化的V-A弱作用下质子俘获μ^-介子几率的公式,并根据电子核子散射的实验结果估计了核子的电荷、磁矩分布对μ^-介子俘获几率中矢量耦合部分贡献的修正。     

Rational compositum genus for a pure cubic field

In non-Abelian fields, to which genus theory does not ordinarily apply, many of the diophantine by-products are still available. For instance, the representability of primes as norms of principal ideals in different fields of the same degree will bear interrelations if the fields belong to a small compositum as do the four subfields of $\text{Q}$(m_∞^1/3, m₀^1/3). This is a generalization of a classical phenomenon for quadratic fields. It is particularly effective when just one prime l ≡ 1 (mod 3) divides m₀m_∞.     

铁矿中微量铜的光谱分析

我们尝试用光谱的方法协助解决分析大量铁矿精矿试样中微量铜(O.05-0.1％)的问题。采用了交流电弧碳电极粉末法,应用现有的设备(中型光谱仪、不纯碳电极、质量低的照相板)进行试验,找出了比较适当的激发条件和分析线对。把空白碳电极加以预燃并在铁矿试样中搀入适当分量的碳粉,可以基本上消减样品在燃烧中的喷爆现象。根据样品的燃烧曲线的研究,选择了适当的曝光时间,使分析的结果不受样品所含铜的化学组成状态的影响。所选定的分析线对当含铜量在0.05-0.3％的范围内时是Cu2824.369-Fe2824.67,当含铜量在0.3-1.0％的范围内时是Cu2824.369-Fe2828.813。根据所得的两条定标曲线作了110个样品的分析,光谱分析结果与化学分析结果的差值在0.02％以下的约占分析样品总数的80％左右。关于含铜量为0.05-0.3％的样品,光谱分析已经可以代替化学分析,并节省大量的人力和物资。     

静电加速器的周期聚焦效应

从理论分析及在电解槽中进行模拟实验测量知道,静电加速器加速管内的电场分布一般不是均匀的,而是有周期性变化的。本文利用微扰法求解了离子束在这种周期场内运动的傍轴轨迹方程,描绘出了离子束在这种场内的轮廓,也求出了表达这个离子光学系统的焦距公式,并讨论了空间电荷效应对离子束的发散作用。     

Considerations on a unified field theory

A geometrical formulation of gravitational and electromagnetic fields is presented for systems composed of point mass charged particles where the charge is small enough that electromagnetic radiation may be neglected. It is assumed that such charges produce a non-negligible contribution to the metric, and that their motion describes geodesics in the total metric which consists of that due to the charge itself and that due to the external environment of the charge. The above, together with several other assumptions yields the customary Einstein-Maxwell relations. It is demonstrated that this construction is not merely a re-statement of the Einstein-Maxwell theory in different terms.     

超子衰变产物的角分布

假设了一定的相互作用哈密顿量,计算了自旋为1/2。而服从狄拉克波动方程的粒子衰变产物的角分布,计算了自旋为3/2而服从赖列泰—许温格波动方程的粒子的衰变产物的角分布。讨论了宇称守恒相互作用和宇称不守恒相互作用强度之间的比例和不对称系数α的关系。指出利用费曼—盖尔曼的普适费米相互作用推导得的Λ超子衰变产物的角分布不对称因子和实验数值一致。指出假使在重正化以后矢量耦合和赝矢量耦合常数不再相等,那末不对称因子的数值可能有相当大的改变。因此准确测定α的数值有助于费曼—盖尔曼普适费米相互作用的重正化效应的研究。服从赖列泰—许温格波动方程,自旋为3/2的粒子衰变产物和实验上得到的的Λ超子衰变产物的角分布不可能符合。这和李政道和杨振宁的一般结论一致。